经典算法实现之归并排序

算法

归并排序有两个基本的操作，一个是分，也就是把原数组划分成两个子数组的过程。另一个是治，它将两个有序数组合并成一个更大的有序数组。

基本思路：将已有序的子序列合并，得到完全有序的序列；即先使每个子序列有序，再使子序列段间有序。若将两个有序表合并成一个有序表，称为二路归并。 归并排序核心步骤：

image-20231102143544582

实现

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/**
 *  \addtogroup sorting Sorting Algorithms
 *  @{
 *  \file
 *  \brief [Merege Sort Algorithm
 *  (MEREGE SORT)](https://en.wikipedia.org/wiki/Merge_sort) implementation
 *
 *  \author [Ayaan Khan](http://github.com/ayaankhan98)
 *
 *  \details
 *  Merge Sort is an efficient, general purpose, comparison
 *  based sorting algorithm.
 *  Merge Sort is a divide and conquer algorithm
 *
 */
#include <iostream>

/**
 *
 * The merge() function is used for merging two halves.
 * The merge(arr, l, m, r) is key process that assumes that
 * arr[l..m] and arr[m+1..r] are sorted and merges the two
 * sorted sub-arrays into one.
 *
 * @param arr - array with two halves arr[l...m] and arr[m+1...r]
 * @param l - left index or start index of first half array
 * @param m - right index or end index of first half array
 *
 * (The second array starts form m+1 and goes till r)
 *
 * @param r - end index or right index of second half array
 */
void merge(int *arr, int l, int m, int r) {
    int i, j, k;
    int n1 = m - l + 1;
    int n2 = r - m;

    int *L = new int[n1], *R = new int[n2];

    for (i = 0; i < n1; i++) L[i] = arr[l + i];
    for (j = 0; j < n2; j++) R[j] = arr[m + 1 + j];

    i = 0;
    j = 0;
    k = l;
    while (i < n1 || j < n2) {
        if (j >= n2 || (i < n1 && L[i] <= R[j])) {
            arr[k] = L[i];
            i++;
        } else {
            arr[k] = R[j];
            j++;
        }
        k++;
    }

    delete[] L;
    delete[] R;
}

/**
 * Merge sort is a divide and conquer algorithm, it divides the
 * input array into two halves and calls itself for the two halves
 * and then calls merge() to merge the two halves
 *
 * @param arr - array to be sorted
 * @param l - left index or start index of array
 * @param r - right index or end index of array
 *
 */
void mergeSort(int *arr, int l, int r) {
    if (l < r) {
        int m = l + (r - l) / 2;
        mergeSort(arr, l, m);
        mergeSort(arr, m + 1, r);
        merge(arr, l, m, r);
    }
}

/**
 * Utility function used to print the array after
 * sorting
 */
void show(int *arr, int size) {
    for (int i = 0; i < size; i++) std::cout << arr[i] << " ";
    std::cout << "\n";
}

/** Main function */
int main() {
    int size;
    std::cout << "Enter the number of elements : ";
    std::cin >> size;
    int *arr = new int[size];
    std::cout << "Enter the unsorted elements : ";
    for (int i = 0; i < size; ++i) {
        std::cin >> arr[i];
    }
    mergeSort(arr, 0, size - 1);
    std::cout << "Sorted array : ";
    show(arr, size);
    delete[] arr;
    return 0;
}
/** @} */